Tipler Solucionario

Chapter 1
Systems of Measurement
Conceptual Problems
*1
•
Determine the Concept The fundamental physical quantities in the SI system include
mass, length, and time. Force, being the product of mass and acceleration, is not a
fundamental quantity. (c) is correct.
2
•
Picture the Problem We can express and simplify the ratio of m/s to m/s2 to determine
the final units.

m
2
s = m ⋅ s= s and (d ) is correct.
m
m ⋅s
2
s

Express and simplify the ratio of
m/s to m/s2:

3
•
Determine the Concept Consulting Table 1-1 we note that the prefix giga
means 109. (c ) is correct.
4
•
Determine the Concept Consulting Table 1-1 we note that the prefix mega
means 106. ( d ) is correct.
*5 •
Determine the Concept Consulting Table 1-1 we note that the prefix pico
means10−12. ( a ) is correct.
6
•
Determine the Concept Counting from left to right and ignoring zeros to the left
of the first nonzero digit, the last significant figure is the first digit that is in doubt. Applyin
criterion, the three zeros after the decimal point are not significant
figures, but the last zero is significant. Hence, there are four significant figures in
this number. (c ) iscorrect.

1

2

Chapter 1

7
•
Determine the Concept Counting from left to right, the last significant figure is
the first digit that is in doubt. Applying this criterion, there are six significant
figures in this number. (e) is correct.
8
•
Determine the Concept The advantage is that the length measure is always with you. The
disadvantage is that arm lengths are not uniform; if you wishto purchase a board of ″two
arm lengths″ it may be longer or shorter than you wish, or else you may have to physically
go to the lumberyard to use your own arm as a measure of length.
9
•
(a) True. You cannot add ″apples to oranges″ or a length (distance traveled) to a volume
(liters of milk).
(b) False. The distance traveled is the product of speed (length/time) multiplied by the
time oftravel (time).
(c) True. Multiplying by any conversion factor is equivalent to multiplying by 1.
Doing so does not change the value of a quantity; it changes its units.

Estimation and Approximation
*10 ••
Picture the Problem Because θ is small, we can approximate it by θ ≈ D/rm
provided that it is in radian measure. We can solve this relationship for the diameter of
the moon.
Expressthe moon’s diameter D in
terms of the angle it subtends at the
earth θ and the earth-moon distance
rm:

D = θ rm

Find θ in radians:

θ = 0.524° ×

Substitute and evaluate D:

D = (0.00915 rad )(384 Mm )

2π rad
= 0.00915 rad
360°

= 3.51 × 106 m

Systems of Measurement

3

*11 ••
Picture the Problem We’ll assume that the sun is made up entirely of hydrogen. Then we
canrelate the mass of the sun to the number of hydrogen atoms and the mass of each.
Express the mass of the sun MS as
the product of the number of
hydrogen atoms NH and the mass of
each atom MH:

M S = NHM H

Solve for NH:

NH =

MS
MH

Substitute numerical values and
evaluate NH:

NH =

1.99 × 1030 kg
= 1.19 × 1057
1.67 × 10 −27 kg

12
••
Picture the Problem Let P representthe population of the United States, r the rate of
consumption and N the number of aluminum cans used annually. The population of the
United States is roughly 3×108 people. Let’s assume that, on average, each person drinks
one can of soft drink every day. The mass of a soft-drink can is approximately
1.8 ×10−2 kg.
(a) Express the number of cans N
used annually in terms of the daily
rate ofconsumption of soft drinks r
and the population P:

N = rP∆t

Substitute numerical values and
approximate N:

⎛ 1can ⎞
8
N =⎜
⎜ person ⋅ d ⎟ 3 × 10 people
⎟
⎝
⎠
⎛
d⎞
× (1 y )⎜ 365.24 ⎟
⎜
y⎟
⎝
⎠

(

≈ 1011 cans
(b) Express the total mass of
aluminum used per year for soft
drink cans M as a function of the
number of cans consumed and the
mass m per can:

M = Nm...